In this paper, a new fast algorithm for path planning and a collision prediction framework for two dimensional dynamically changing environments are introduced. The method is called Time Distance (TD) and benefits from the space-time space idea. First, the TD concept is defined as the time interval that must be spent in order for an object to reach another object or a location. Next, TD functions are derived as a function of location, velocity and geometry of objects. To construct the configuration-time space, TD functions in conjunction with another function named "Z-Infinity" are exploited. Finally, an explicit formula for creating the length optimal collision free path is presented. Length optimization in this formula is achieved using a function named "Route Function" which minimizes a cost function. Performance of the path planning algorithm is evaluated in simulations. Comparisons indicate that the algorithm is fast enough and capable to generate length optimal paths as the most effective methods do. Finally, as another usage of the TD functions, a collision prediction framework is presented. This framework consists of an explicit function which is a function of TD functions and calculates the TD of the vehicle with respect to all objects of the environment.

翻译：在本文中，介绍了一种新的快速路径规划算法和二维动态变化环境下的碰撞预测框架。该方法称为时间距离 (TD)，并利用了时空空间的思想。首先，TD的概念被定义为一个对象到达另一个对象或位置所需的时间间隔。接下来，利用对象的位置、速度和几何形状来派生TD函数。为了构造配置-时间空间，TD函数与另一个名为“Z-Infinity”的函数相结合。最后，提出了一个明确的公式来创建最优化的无碰撞路径。通过使用名为“路径函数”的函数来最小化成本函数，可以实现优化路径长度。路径规划算法的性能在模拟中进行评估。比较表明，该算法足够快速且能够生成长度最优化的路径，就像最有效的方法一样。最后，作为TD函数的另一种用途，提出了一种碰撞预测框架。该框架由一个明确的函数组成，该函数是TD函数的函数，用于计算车辆相对于环境中所有对象的TD。